The light turns on but the screen is black how do I fix it?

Ignore "Jack Dye's " solution that is not true the psp is a good system. It seems like your issue is that you have what is called a "BRICKED PSP".You probably tried installing custom firmware on your psp which allows you to save homebrew games for free on your psp or something similiar to that. But dont worry there is a way to fix it, there is the easy solution which is too buy a new one :( which if your like me you dont have the money.
The other solution is too buy what is called a "PANDORAS BATTERY" which simplified reverse engineers the psp and "UNBRICKS" .there is even one more solution to do which is make your own pandoras battery. Im not going into more detail, Please do research on the tips i gave you and contact me for more info. Thanks PLEASE GIVE ME A GOOD RATING SO I CAN GET MY RANK UP

Rumor has it allot of psp's are corrupt get it sent back or find repair shop